A technique enables efficient access to logical unit numbers (luns) or virtual disks (vdisks) stored on a storage system, such as a multi-protocol storage appliance. The technique allows a grouping of initiators by a "human friendly" logical name that is mapped to a lun or vdisk on the storage appliance. The initiators are clients operating in, e.g., a storage area network (SAN) environment that initiate requests for the vdisk using block-based access protocols, such as the Small Computer Systems Interface (SCSI) protocol encapsulated over TCP/IP (iSCSI) or over fibre channel (FCP). The technique enables access to the vdisk by all initiators that are members of the initiator group (igroup). An igroup is a logical named entity that is assigned to one or more addresses associated with one or more initiators. These addresses may comprise fibre channel (FC) world wide name (WWN) or iSCSI name identifiers (IDs). Therefore, rather than having to specify these IDs when desiring access to a vdisk, an initiator need only specify the human friendly name of the igroup.